Kinetic simulations of the Chodura and Debye sheaths for magnetic fields with grazing incidence

Coulette, David; Manfredi, Giovanni

doi:10.1088/0741-3335/58/2/025008

Cited by 35 publications

(54 citation statements)

References 22 publications

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“…in the numerator of k 3/2 is equal to zero, which means that k 3/2 = 0 and the correct form of the potential at x → ∞ is given by equation (112). The value of k 2 in the cold ion limit, k 2,cold , is obtained from (111) At sufficiently large x, C 2,cold can be neglected and Chodura's result for the scaling of the potential at the magnetic presheath entrance x → ∞ is recovered (this scaling is obtained from Chodura's paper [10] by combining equations (22), (23), and the equation immediately after (24), and noting that Chodura's notation is ψ = π/2 − α and his derivation is valid for general ψ).…”

Section: Appendix A2 Gyrophase Expansionmentioning

confidence: 99%

Solution to a collisionless shallow-angle magnetic presheath with kinetic ions

Geraldini

Parra

Militello

2018

Plasma Phys. Control. Fusion

110

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Using a kinetic model for the ions and adiabatic electrons, we solve a steady state, electron-repelling magnetic presheath in which a uniform magnetic field makes a small angle α 1 (in radians) with the wall. The presheath characteristic thickness is the typical ion gyroradius ρ i . The Debye length λ D and the collisional mean free path of an ion λ mfp satisfy the ordering λ D ρ i αλ mfp , so a quasineutral and collisionless model is used. We assume that the electrostatic potential is a function only of distance from the wall, and it varies over the scale ρ i . Using the expansion in α 1, we derive an analytical expression for the ion density that only depends on the ion distribution function at the entrance of the magnetic presheath and the electrostatic potential profile. Importantly, we have added the crucial contribution of the orbits in the region near the wall. By imposing the quasineutrality equation, we derive a condition that the ion distribution function must satisfy at the magnetic presheath entrance -the kinetic equivalent of the Chodura condition. Using an ion distribution function at the entrance of the magnetic presheath that satisfies the kinetic Chodura condition, we find numerical solutions for the self-consistent electrostatic potential, ion density and flow across the magnetic presheath for several values of α. Our numerical results also include the distribution of ion velocities at the Debye sheath entrance. We find that at small values of α there are substantially fewer ions travelling with a large normal component of the velocity into the wall.

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Section: Appendix A2 Gyrophase Expansionmentioning

confidence: 99%

Solution to a collisionless shallow-angle magnetic presheath with kinetic ions

Geraldini

Parra

Militello

2018

Plasma Phys. Control. Fusion

110

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“…Close to the wall in the magnetic presheath, the time it takes for an ion to intersect the wall is a typical ion gyroperiod, while the time it takes for an electron (due to its much smaller Larmor radius) is given by its faster streaming along the field line towards the wall, as shown in Figure 3. The criterion that must be satisfied for electrons to reach the wall faster, leading to a negatively charged wall, is α m e /m i 0.02 ( 1 • ) [31,35], where m e and m i are the electron and ion mass respectively, and the estimate is made using the mass of a deuterium ion. Hence, we assume m e m i α 1.…”

Section: Orderingsmentioning

confidence: 99%

“…Note that if we takeĒ and E both positive and only look at the region where both x and dφ/dx are positive, the electric field is directed towards x = 0 (the wall) and increasing as x gets smaller, which is qualitatively similar to the electric field in the magnetic presheath. In this section, we use equations (26), (27), (30), (31) and (33), which are valid for a general electric field, in order to solve the zeroth order problem with the linear electric field (E.1). The effective potential in the linear electric field is…”

Section: Appendix E the Zeroth Order Problem With A Linear Electric mentioning

confidence: 99%

Gyrokinetic treatment of a grazing angle magnetic presheath

Geraldini

Parra

Militello

2017

Plasma Phys. Control. Fusion

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Abstract. We develop a gyrokinetic treatment for ions in the magnetic presheath, close to the plasma-wall boundary. We focus on magnetic presheaths with a small magnetic field to wall angle, α 1 (in radians). Characteristic lengths perpendicular to the wall in such a magnetic presheath scale with the typical ion Larmor orbit size, ρ i . The smallest scale length associated with variations parallel to the wall is taken to be across the magnetic field, and ordered l = ρ i /δ, where δ 1 is assumed. The scale lengths along the magnetic field line are assumed so long that variations associated with this direction are neglected. These orderings are consistent with what we expect close to the divertor target of a tokamak. We allow for a strong component of the electric field E in the direction normal to the electron repelling wall, with strong variation in the same direction. The large change of the electric field over an ion Larmor radius distorts the orbit so that it is not circular. We solve for the lowest order orbits by identifying coordinates, which consist of constants of integration, an adiabatic invariant and a gyrophase, associated with periodic ion motion in the system with α = δ = 0. By using these new coordinates as variables in the limit α ∼ δ 1, we obtain a generalized ion gyrokinetic equation. We find another quantity that is conserved to first order and use this to simplify the gyrokinetic equation, solving it in the case of a collisionless magnetic presheath. Assuming a Boltzmann response for the electrons, a form of the quasineutrality equation that exploits the change of variables is derived. The gyrokinetic and quasineutrality equations give the ion distribution function and electrostatic potential in the magnetic presheath if the entrance boundary condition is specified.

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“…Instead of using the PIC method, our code employs a continuum kinetic method for its inherent lack of statistical noise and good resolution of distribution functions. These advantages are particularly valuable for studies involving sheaths, as shown by other recent works [46,47,48]. Here, the number of particles per unit phase space volume fs(x,vs,t) for each charge species s is calculated by advancing the kinetic Boltzmann Transport Equation explicitly over a uniform finite difference 1D-1V grid where the velocity direction is normal to the electrodes (vs = vs,x in this section).…”

Section: A Continuum Kinetic Codementioning

confidence: 99%

Alternative model of space-charge-limited thermionic current flow through a plasma

Campanell

2018

Phys. Rev. E

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It is widely assumed that thermionic current flow through a plasma is limited by a "space-charge-limited" (SCL) cathode sheath that consumes the hot cathode's negative bias and accelerates upstream ions into the cathode. Here, we formulate a fundamentally different current-limited mode. In the "inverse" mode, the potentials of both electrodes are above the plasma potential, so that the plasma ions are confined. The bias is consumed by the anode sheath. There is no potential gradient in the neutral plasma region from resistivity or presheath. The inverse cathode sheath pulls some thermoelectrons back to the cathode, thereby limiting the circuit current. Thermoelectrons entering the zero-field plasma region that undergo collisions may also be sent back to the cathode, further attenuating the circuit current. In planar geometry, the plasma density is shown to vary linearly across the electrode gap. A continuum kinetic planar plasma diode simulation model is set up to compare the properties of current modes with classical, conventional SCL, and inverse cathode sheaths. SCL modes can exist only if charge-exchange collisions are turned off in the potential well of the virtual cathode to prevent ion trapping. With the collisions, the current-limited equilibrium must be inverse. Inverse operating modes should therefore be present or possible in many plasma devices that rely on hot cathodes. Evidence from past experiments is discussed. The inverse mode may offer opportunities to minimize sputtering and power consumption that were not previously explored due to the common assumption of SCL sheaths.

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Kinetic simulations of the Chodura and Debye sheaths for magnetic fields with grazing incidence

Cited by 35 publications

References 22 publications

Solution to a collisionless shallow-angle magnetic presheath with kinetic ions

Solution to a collisionless shallow-angle magnetic presheath with kinetic ions

Gyrokinetic treatment of a grazing angle magnetic presheath

Alternative model of space-charge-limited thermionic current flow through a plasma

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